Table 4 The maximum norm errors and spatial convergence order with fixed time step \(\pmb{\tau=\frac{1}{1{,}000}}\)
J | p  = 2 | p  = 3 | p  = 6 | |||
|---|---|---|---|---|---|---|
\(\boldsymbol {\|u^{n}-U^{n}\|_{\infty, h}}\) | order1 | \(\boldsymbol {\|u^{n}-U^{n}\| _{\infty, h}}\) | order1 | \(\boldsymbol {\|u^{n}-U^{n}\|_{\infty, h}}\) | order1 | |
125 | 9.7465 × 10−4 | – | 2.9741 × 10−3 | − | 4.2113 × 10−3 | – |
250 | 7.0687 × 10−5 | 3.7854 | 2.3162 × 10−4 | 3.6826 | 3.5045 × 10−4 | 3.5870 |
500 | 4.5932 × 10−6 | 3.9439 | 1.5359 × 10−5 | 3.9164 | 2.6008 × 10−5 | 3.7522 |
1,000 | 2.9062 × 10−7 | 3.9823 | 9.9102 × 10−7 | 3.9540 | 1.6700 × 10−6 | 3.9610 |